Advanced/Notes 8.1

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Advanced/Notes 8.1

  1. 1. Chapter 8Rotational Motion
  2. 2. Angular Quantities How do I define angular quantities?
  3. 3. Rotational Motion Purely rotational : all points on the object move in circles The circle moves around an axis of rotation
  4. 4. Angular Quantities
  5. 5. Radian Review Radian: The angle subtended by an arc whose angle length is equal to the radius (?!) 1 revolution = 360° = 2π radians A bike wheel rotates 4.50 revolutions. How many radians has it rotated?
  6. 6. ExampleA particular bird’s eyecan just distinguishobjects that subtend anangle no smaller than 3x 10-4 rad. (a) Howmany degrees is this?(b) How small an objectcan the bird justdistinguish when flyingat a height of 100m?
  7. 7. Angular Kinematics
  8. 8. Angular Kinematics
  9. 9. Relating Angular and LinearVelocity
  10. 10. Relating Angular and LinearVelocity Objects farther from the axis of rotation will move faster
  11. 11. Different Accelerations
  12. 12. Without Slipping Must have static friction between the rolling object and the surface Tangential accelerations and velocities must be the same ◦ # 13 on HW
  13. 13. Relating Linear and RotationalQuantities
  14. 14. ExampleA carousel is initially at rest. At t = 0, it is given a constantangular acceleration α = 0.060 rad/s2, which increases itsangular velocity for 8.0 s. At t = 8.0 s, determine the followingquantities:a) The angular velocity of the carouselb) The linear velocity of a child located 2.5 m from the center, Pc) The tangential (linear) acceleration of that childd) The centripetal acceleration of the childe) The total linear acceleration of the child
  15. 15. Timing Review
  16. 16. Homework Read Section 8.1 Do Problems # 1, 3 – 8, 12, 13 on page 219

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